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ABSTRACT

We present a theoretical framework of a new problem representation.
The quotient structure model is presented for representing different
grain-size worlds. Our aim is to explore the relationship between
different grain-size worlds and reveal the essence of human
hierarchical problem solving skill. The motivation of the research
stems from our belief that more human-like characteristics in problem
solving should be involved in a formal representation to achieve
better performance for computer- based problem solver.

To illustrate the role of the hierarchy we make use of topologic and
semi-order space as expository tools and show that
attribute-preserving among different grain-size worlds is of central
importance in hierarchical problem solving. The complexity of
hierarchical problem solving by using the quotient structure model is
analyzed. The main goal of using hierarchical problem solving is to
reduce the computational complexity. The applications of the theory to
heuristic search, robot planning and function optimization are
discussed.

Based on the theory, the combination of information from different
levels of abstraction (granularities) is discussed. Some combination
criteria are given. From one of these criteria we reveal the principle
of the Dempster-Shafer combination rule in uncertain management. The
same theory can be used to analyze the interdependency between
quantitative, qualitative, fuzzy and other uncertain reasoning.